Open Set

So, let’s say you are a math teacher who teaches the way you were taught. You explain the concepts as clearly as you know how. You present the steps students need to solve the problems, keeping it manageable and simple. You ask students to do independent practice during class time because you know that what they don’t practice, they don’t actually learn. You go over answers together, so students can learn from their mistakes. 

But you’ve decided that you want to make your class a little more “inquiry-based.” You’ve heard that there are other ideas out there, and you want to see how they will work. 

Where do you start? What’s the first step to having a slightly more “inquiry-based” class? 

Right now, my opinion is that the best way to start is with a 5 – 10 minute activity towards the start of the period. Why that? First, at the start of the lesson, the kids are the most open to new ideas. When the period starts, they have the energy from walking into the room, they are curious about what’s going to happen today (or, at least, as curious as they are going to be). 

Also, at this stage in the lesson, the students in that class are closest to each other in terms of background knowledge. If you want to provide a chance for students to share ideas with each other, it’s really helpful if everyone has to engage in the problem-solving together. Figuring out how to solve a problem is different than applying a familiar technique. You want students to bring their own ideas to the table, to know that their thinking is valued.

Once you start to teach a new topic, some kids catch on to what you are saying, and some are lost. At that point, group work has a different dynamic. The students who understand the math will be explaining what to do to those who don’t yet get it. Now, don’t get me wrong: there is a huge value in this type of group work! But it’s different than when everyone needs to help each other to come up with an answer. I want to give students an opportunity to let their own ideas shine, and hopefully let all students feel like they could have a valuable idea. 

Before you teach them the topic, everyone has some knowledge gaps. This is a chance to utilize those knowledge gaps to bring in student thinking. (Unless you live in a town with significant Russian School of Math infiltration. Then finding a way to bring your class together is basically a lost cause, unless your school tracks.)   

So then, what does this short activity near the start of class look like? Well, it has to be something that students can figure out, but they don’t already know. And it should be related to what you are about to do that day, so they can see the connection between the ideas they had and the material they learn. Extra points if you can add a bit of a puzzle feel, or connections to the real world, or maybe make it concrete (as in physical). 

The example I came up with the other day was for a pre-calc class. They were about to learn about radian measure. The teacher always starts that lesson with a short activity using string to connect the radius of a circle to its circumference. (Love it!!) Then he starts to get into how 2pi radii is the whole circle, but half a circle is pi radii, and a quarter is pi/2. But that’s just enough information to let the students explore and see where they can go with it! 

My recommendation was to stop there, and create a worksheet that would get students to toy with this idea. Something like this: 

And then, after 5 minutes of group work, and 5 minutes of discussion, go back to your regularly-scheduled lesson. 

My school recently purchased the Reveal textbooks for math classes. Reveal has a “Launch” at the start of each lesson which is similar to this idea. It presents a situation that uses the math we are about to learn, and gives students a chance to come up with their own ideas, before the teacher presents the examples and explains the concepts. It’s a way to play around with student voice and inquiry, but without needing to jump in with both feet, or change your beliefs about how math is learned. 

I’m going to try this model with the teachers I work with, if they are “inquiry-curious.” I plan to update on how this works out in later posts.